Simulation of transition and turbulence decay in the Taylor–Green vortex

Conventional large-eddy simulation (LES) and monotone integrated LES (MILES) are tested in emulating the dynamics of transition to turbulence in the Taylor–Green vortex (TGV). A variety of subgrid scale (SGS) models and high-resolution numerical methods are implemented in the framework of both incompressible and compressible fluid flow equations. Comparisons of the evolution of characteristic TGV integral measures are made with previously reported and new direct numerical simulation (DNS) data. The computations demonstrate that the convective numerical diffusion effects in the MILES methods can consistently capture the physics of flow transition and turbulence decay without resorting to an explicit SGS model, while providing accurate prediction of established theoretical findings for the kinetic energy dissipation, energy spectra, enstrophy and kinetic energy decay. All approaches tested provided fairly robust computational frameworks.

[1]  Jinhee Jeong,et al.  On the identification of a vortex , 1995, Journal of Fluid Mechanics.

[2]  P. Sagaut.  Large Eddy Simulation for Incompressible Flows , 2001 .

[3]  D. Drikakis.  Advances in turbulent flow computations using high-resolution methods , 2003 .

[4]  B. V. Leer,et al.  Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's method , 1979 .

[5]  B. V. Leer,et al.  Towards the ultimate conservative difference scheme. IV. A new approach to numerical convection , 1977 .

[6]  F. Grinstein,et al.  Large Eddy simulation of high-Reynolds-number free and wall-bounded flows , 2002 .

[7]  William J. Rider,et al.  Modeling turbulent flow with implicit LES , 2006 .

[8]  L. Skrbek,et al.  On the decay of homogeneous isotropic turbulence , 2000 .

[9]  Christer Fureby,et al.  From canonical to complex flows: Recent progress on monotonically integrated LES , 2004, Computing in Science & Engineering.

[10]  Marcel Lesieur,et al.  3D isotropic turbulence at very high Reynolds numbers: EDQNM study , 2000 .

[11]  L. Margolin,et al.  A rationale for implicit turbulence modelling , 2001 .

[12]  Steven A. Orszag,et al.  Spontaneous singularity in three-dimensional inviscid, Incompressible flow , 1980 .

[13]  J. Smagorinsky,et al.  GENERAL CIRCULATION EXPERIMENTS WITH THE PRIMITIVE EQUATIONS , 1963 .

[14]  S. Orszag,et al.  Small-scale structure of the Taylor–Green vortex , 1983, Journal of Fluid Mechanics.

[15]  Leland Jameson,et al.  Numerical Convergence Study of Nearly Incompressible, Inviscid Taylor–Green Vortex Flow , 2005, J. Sci. Comput..

[16]  W. Rider,et al.  High-Resolution Methods for Incompressible and Low-Speed Flows , 2004 .

[17]  Javier Jiménez,et al.  The structure of intense vorticity in isotropic turbulence , 1993, Journal of Fluid Mechanics.

[18]  R. D. Richtmyer,et al.  A Method for the Numerical Calculation of Hydrodynamic Shocks , 1950 .

[19]  P. Moin,et al.  A dynamic subgrid‐scale eddy viscosity model , 1990 .

[20]  J. Steinhoff,et al.  Modification of the Euler equations for ‘‘vorticity confinement’’: Application to the computation of interacting vortex rings , 1994 .

[21]  P. Smolarkiewicz,et al.  Effective eddy viscosities in implicit large eddy simulations of turbulent flows , 2003 .

[22]  J. P. Boris,et al.  New insights into large eddy simulation , 1992 .

[23]  J. Ferziger,et al.  Improved subgrid-scale models for large-eddy simulation , 1980 .

[24]  Paul R. Woodward,et al.  High-resolution simulations of compressible convection using the piecewise-parabolic method , 1994 .

[25]  D. Youngs,et al.  Three-dimensional numerical simulation of turbulent mixing by Rayleigh-Taylor instability , 1991 .

[26]  Jay P. Boris,et al.  On large eddy simulation using subgrid turbulence models Comment 1 , 1990 .

[27]  Paul R. Woodward,et al.  Kolmogorov‐like spectra in decaying three‐dimensional supersonic flows , 1994 .

[28]  Nikolaus A. Adams,et al.  An adaptive local deconvolution method for implicit LES , 2005, J. Comput. Phys..

[29]  M. Brachet.  Direct simulation of three-dimensional turbulence in the Taylor–Green vortex , 1991 .

[30]  P. Smolarkiewicz.  A Fully Multidimensional Positive Definite Advection Transport Algorithm with Small Implicit Diffusion , 1984 .

[31]  U. Schumann.  Subgrid Scale Model for Finite Difference Simulations of Turbulent Flows in Plane Channels and Annuli , 1975 .

[32]  Eric D. Siggia,et al.  Numerical study of small-scale intermittency in three-dimensional turbulence , 1981, Journal of Fluid Mechanics.

[33]  Joseph Smagorjnsky,et al.  The Beginnings of Numerical Weather Prediction and General Circulation Modeling: Early Recollections , 1983 .

[34]  Leif Persson,et al.  On large eddy simulation of high Reynolds number wall bounded flows , 2004 .

[35]  P. Sagaut,et al.  On the Use of Shock-Capturing Schemes for Large-Eddy Simulation , 1999 .

[36]  F. Grinstein,et al.  Monotonically integrated large eddy simulation of free shear flows , 1999 .

[37]  Jay P. Boris,et al.  Flux-corrected transport. I. SHASTA, a fluid transport algorithm that works , 1973 .

[38]  A. Gosman,et al.  Solution of the implicitly discretised reacting flow equations by operator-splitting , 1986 .

[39]  C. R. DeVore,et al.  An Improved Limiter for Multidimensional Flux-Corrected Transport, , 1998 .

[40]  U. Piomelli,et al.  Turbulent structures in accelerating boundary layers , 2000 .